Polaronic Effects of an Exciton in a Cylindrical Quantum Wire

The effects of exciton-optical phonon interaction on the binding energy and the total and reduced effective masses of an exciton in a cylindrical quantum wire have been investigated. Weadopt a perturbative-PLL[T.D. Lee, F. Low, and D. Pines, Phys. Rev. B90 (1953) 297] technique to construct an effectiveHamiltonian and then use a variational solution to deal withthe exciton-phonon system. The interactions of exciton with thelongitudinal-optical phonon and the surface-optical phononhave been taken into consideration. The numericalcalculations for GaAs show that the influences of phonon modes onthe exciton in a quasi-one-dimensional quantum wire areconsiderable and should not be neglected. Moreover the numericalresults for heavy- and light-hole exciton are obtained, whichshow that the polaronic effects on two types of excitons are verydifferent but both depend heavily on the sizes of the wire.